Abstract

A method to produce patterned, controlled size triangula
tion of Boundary Representations is presented. Although
the produced patterned triangulations are not immediately
suited for fast visualization, they were used in Fixed Grid
Finite Element Analysis, and do provide a control on the
aspect ratio or shape factor of the triangles produced. The
method presented ﬁrst calculates a triangulation in the pa
rameter space of the faces in which the B-Rep is partitioned
and then maps it to 3D space. Special emphasis is set in en
suring that the triangulations of neighboring faces meet in
a seamless manner, therefore ensuring that a borderless C2
2-manifold would have as triangulation a C0
borderless 2
manifold. The method works properly under the conditions
(i) the parametric form of the face is a 1-1 function, (ii) the
parametric pre-image of a parametric face is a connected
region, and (iii) the user-requested sampling frequency (
samples per length unit ) is higher than twice the spatial
frequency of the features in the B-Rep ( thus respecting the
Nyquist principle ). As the conditions (i) and (ii) are pos
sible under face reparameterization or sub-division and the
condition (iii) is the minimum that a triangulation should
comply with, the method is deemed as generally applica
ble.